R. Fürth’s 1933 paper “On certain relations between classical statistics and quantum mechanics” [“Über einige Beziehungen zwischen klassischer Statistik und Quantenmechanik”, Zeitschrift für Physik, 81 143–162]

We present a translation of the 1933 paper by R. Fürth in which a profound analogy between quantum fluctuations and Brownian motion is pointed out. Fürth highlights the existence of uncertainty relations involving the variance of a statistically conserved quantity of a non-equilibrium thermodynamic indicator and the variance of the corresponding current velocity. The phenomenon is entirely classical and traces back to the effect of a fluctuating environment on a measured system. In some sense, Fürth’s paper also opened the way to the stochastic methods of quantization developed almost 30 years later by Edward Nelson and others.